I do get your point, and it's a good one. My opinion about allowing the user the luxury of having selected their preferred reading environment isn't so inflexible to say that you shouldn't afford users some concessions in a scenario such as this.
On my PC, I of course do see a scrollbar. In fact, I probably would not at first even realize that I need to instruct viewers on other platforms to interact with the content in any unusual manner. But once aware of it, given the capability to design my content differently to avoid the situation described, I would go with that. Failing that option, I would probably just put instructions in as you've done here.
I would fairly steadfastly refuse to implement my own scrollbar functionality because I'd likely fail to implement that in a manner all users on all devices would understand intuitively.
For the majority of scenarios, the browsers' default behavior will match the users' expectations and they will be able to consume the content I've created in the fashion with which they are accustomed.
As an aside, this conversation reminds me that legacy versions of IE (and maybe current versions; I've not checked) allowed one to affect the appearance of the browser's scrollbar through CSS.